Control apparatus



Sept. 1, 1970 H. M. l. GRAEFE ETAI- 3,526,754

CONTROL APPARATUS 3 Sheets-Sheet 1 Filed July 1, 1968 INVENTORS HANS MAXINGFRIED GRAEFE ROLF DIETER \PFEIFER HELMUT HEINRICH SPAHN BY ATTORNEY Spt 1 H. M. l. GRAEFE ET AL CONTROL APPARATUS Filed July 1, 1968 5SheetsSheet 2 FIG. '4

INVENTORS HANS MAX INGFRIED GRAEFE ROLF DIETERPFEIFER HELMUT HEINRICHSPAHN MLM ATTORNEY United States Patent Cffice 3,526,754 Patented Sept.1, 1970 US. Cl. 235-615 11 Claims ABSTRACT OF THE DISCLOSURE A dynamicbiaxial lead computer for the lateral and vertical lead angles oftank-mounted anti-aircraft guns.

SUMMARY OF THE INVENTION The present invention pertains to the field ofgeometrical instruments and, more particularly, to automatic gunmovement compensators.

The present invention is intended for use with fire control systemsincluding a biaxially directionable weapon and a biaxially directionablesight or fire director, both mounted on a mobile platform such as a tankor ship, and interconnected electrically as by servo systems such thatthe sight line determines the weapon line of fire.

The present disclosure concerns a lead angle computer to be interposedin the electrical interconnections to automatically provide an angle oflead between the weapon line of fire and the sight line to compensatefor target speed, direction, projectile speed, and projectile ballisticsor trajectory.

The present invention provides a lead angle computer especially suitedto anti-aircraft guns, mounted on tanks or ships, which are directedtoward and which follow a moving target. The invention evaluates thenecessary lead angles with respect to the sight line. The lead angle canbe computed by using the lateral lead angle together with the verticallead angle or the lateral lead angle together with the whole elevationangle. The target may be aligned with the sight by means of adirectioning handle positioned by the operator. Movements of thesupporting frame as would be found with ship or tank mounting can becompensated for by an automatically operating target holding system.

The automatic target holding system would be a necessary element in anapplication of the present invention wherein an anti-aircraft weapon ismounted on a rotatable turret containing a primary weapon. For thisembodiment, it is desired that the secondary weapon be turned andelevated without regard to the motion of the turret which directs theprimary weapon. The fire director or sight is also mounted on theturret. The stabilization system provides that the line of sight remainsstable with respect to a space reference in spite of turret or vehiclemovements without requiring corrections by the gun operator.

It is, of course, also desired that the method of stabilization notaffect operation and direction of the weapon by the operator. To thisend, the preferred embodiment utilizes direct stabilization of the firedirector which in turn maintains the weapon in alignment. The systemconsists of a directioning handle affected by gyros necessary forstabilization controlling the fire director or sight. The lead anglecomputer is connected between the fire director and the weapon directingmechanism.

The lead angle is computed in two components, the lateral lead angle 6and the vertical lead angle 6 For purposes of determination it isassumed that the target moves with a constant V along a straight linepath and that the projectile follows a straight line path with adecreasing speed, determinable from a firing table for the particularkind of ammunition used. Curvature of the path of the projectile underthe influence of gravity is compensated for by enlarging a to allow forthe ballistic super elevation A6.

The average projectile speed V due to the decreasing instantaneousspeed, depends on the distance e which the projectile must travel toreach the target.

According to the invention, transducers generate signals proportional tothe angular rates of the sight line in the lateral direction (C and thevertical direction (C In one embodiment of the invention, the signalsare produced by a rate gyro firmly aligned with the sight line. The rategyro for the lateral angular speed simultaneously follows the turningmotion in the vertical direction. An alternate embodiment derives thesignals from a directioning handle for the sight line.

The angular rate signals are combined with signals proportional to thetarget distance e along the sight line r and the average projectilespeed V for determination of the vertical and lateral lead angles 6 and6 of the weapon with respect to the sight line which is assumed to beconstantly directed to the target. The lateral and vertical lead angleequations are e sin 6 C' (1) and For small lead angles:

cos 6 1 sin 6 5 The equations for the lateral and vertical lead anglestherefore become and sin 6 sin 58 K cos 0 For small angles 5 a N a K cos0 cos a H is the elevation angle of the weapon with respect to theturning plane of the turret and B is the elevation angle of the sightline with respect to the turning plane of the turret.

The invention provides a method of continuous evaluation of the targetdistance e. An integration arrangement is used wherein the initialdistance e is adjusted and the distance thereafter is computed dependingon the angle a of the sight line r with respect to the line at the timeof initial distance estimate. The instantaneous distance with respect tothe initial distance is computed according to the equation care of bythe. stabilization system.

An important feature of the present invention lies in the fact thatevaluation of the lead quantities not only considers motions of thesight line in following the target but also that when the target is keptalong the sight line, the lead quantities are automatically correctedfor rotational motions of the vehicle around the sight line. Turningmotions of the vehicle around other axes are taken An additional featureof the present invention lies in the modification of the vertical leadangle 6 of the weapon to allow for the ballistic super-elevation A ofthe munition:

wherein g=earths acceleration,

6 =the elevation angle of the sight line with respect to the turningplane of the turret carrying the weapon,

e=target distance along the sight line r, and

v =average projectile speed along the projectile path.

With consideration of the ballistic super-elevation, the total verticallead angle 6 becomes It is evident from Equations 1 and 2 that thetarget diestance enters proportionally into the evaluated lead angles.Errors in distance (dependent on measurement of the initial distance ealfect the lead angle in their full magnitude. The present inventionprovides an improvement whereby the hit probability may be increased toallow for inaccuracies in the distance measurements. A periodicallyvarying signal is heterodyned to the calculated lead signals. Theperiodically varying signal is of such an amplitude to cause sweeping ofthe target area to allow for errors in distance measurement.

The objects of the present invention are:

To provide apparatus for and methods of fire control for ordnancedevices, particular anti-aircraft ordnance.

To provide apparatus for and methods of computation of lead angles foranti-aircraft weapons.

To provide a lead computer having means for continuous evaluation of thetarget distance.

To provide a lead computer which corrects for rotational motions of agun platform about the axis of the sight line.

To provide means for modification of the vertical lead angle to allowfor the ballistic super-elevation of the munition.

To provide means for increasing the hit probability to allow forinaccuracies in distance measurements.

Other advantages of the present invention will become apparent from thespecification taken in connection with the drawings.

In the drawings the following reference symbols are used to facilitatean understanding of the invention.

Z position of the target at the moment of firing r sight line at themoment of firing e target distance along the sight line P position ofthe weapon T point at Which the projectile contacts the target sprojectile path 2 projectile flight distance along s t projectile flighttime v average projectile speed v target speed (assumed constant) AEturning plane of turret BE reference plane defined by sight line r and aline perpendicular to the line r, at point P, in plane AE. This plane isseen as a line parallel to the turning plane AE of the turret whenviewed along the sight line r. (horizontal line in a cross hair sight) aangle passed by sight line with respect to sight line position at timeof initial distance C input FE plane defined by target path f and weaponposition A angle between target path 1 and field of view plane GE 0elevation angle of sight line with respect to turning plane of turret 6total lead angle between projectile path s and sight line r a laterallead angle component 8 vertical lead angle component 0 elevation angleofweapon with respect tothe turning plane of the turret K inclinationangle of projection of target path 1 on plane GE with respect toreference plane BE.

FIG. 1 is a view perpendicular to plane FE;

FIG. 2 is a spatial representation of the pertinent geometry necessaryfor an explanation of the invention;

FIGS. 3A and 3B represent the field of view of the gun pointer as seenthrough the sight with mutually perpendicular cross hairs F and F FIG. 4is a vector diagram illustrating the geometrical addition of twoperpendicular components of the directioning signal C; and,

FIG. 5 is a block diagram of the preferred embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT In the preferred embodimentshown in FIG. 5, a signal C proportional to the lateral angular speed ofthe sight line is applied to an input terminal 1. A signal Cproportional to the vertical angular speed of the sight line isconnected to an input terminal 2. Inputs 1 and 2 are further connectedto the input of a geometrical addition circuit 3 having an output lead4. Output lead 4 is further connected to the input of an integratorcircuit 5 having an output connected to a sine transformer 8 by lead 31.The output of sine transformer 8 is connected by lead 32 to a firstinput of a divider circuit 9 having an output lead 26 and a secondinput.

An input terminal 30 is connected to a constant signal source U Inputterminal 30 is connected to the input of an integrator circuit 7, theoutput of which is connected by means of a lead 33 to one of two inputsof a multiplier circuit 6. A lead 34 connects output terminal 4 ofcircuit 3 to the second input of the multiplier circuit 6. The output ofmultiplier circuit 6 is connected through a lead 35 to the second inputof divider circuit 9'. The output of divider circuit 9 is connected to afirst input of a multiplier circuit 11 through a lead 26.

An input terminal 10 is connected to a signal 2 proportional to theinitial range of the target. Input terminal 10 is further connected to asine modulator 12 having an output lead 27 connected to a second inputof multiplier circuit 11. The output of multiplier circuit 11 isconnected to the input of a non-linear circuit 13 by means of lead 36-.The output of non-linear circuit 13 is connected to a first input of amultiplier circuit 14 (having a second input) through a lead 37. A lead38 connects input terminal 1 to the second input of a multiplier circuit14. The output of multiplier circuit 14 is connected to an input of adivider circuit 20 through a lead 39.

A mechanical input 16 to a resolver 17 is driven by the elevationmechanism of the sight. The output of resolver 17 is coupled to ademodulator circuit 18 through a lead 40. The demodulator circuit 18output is connected to an amplifier circuit 22 through a lead 41. Theoutput of demodulator circuit 18 is also coupled through a lead 19 to asecond input of divider circuit 20. The output of divider circuit 20 isconducted through a lead 21 to the turret drive to align the weapon withreference to the sight line in accordance with the calculated laterallead angle.

The output of amplifier 22 is connected through a lead 24 to an input ofa summing amplifier 23. A second input of summing amplifier 23 isconnected to the second input terminal for the vertical angular speedsignal through a lead 25. The output of summing amplifier 23 isconnected through a lead 42 to an input of a multiplier circuit 15. Asecond input to multiplier circuit 15 is connected to the output ofnon-linear amplifier 13 through a lead 43. The output of multipliercircuit 15 is conducted through a lead 28 to the elevation mechanism forthe weapon to control the elevation with respect to the sight line in accordance with the calculated vertical lead angle.

OPERATION With reference to FIG. 1, the distance 1 traveled by thetarget during the time of projectile flight along the path s and theaverage projectile speed VG may be computed in the following equations:

f=l l=vzG (7 Referring to FIG. 2, the following lead angle relations canbe derived:

DZ s1n 6 HG cos A cos x (9) It will be noted that Equations 8 and 9 forthe lead angles and 5 have no dependence upon the position of the weaponor the elevation angle H When following a target through the opticalsight, the target speed vector V is projected on the field of view planeGE. The apparent velocity as seen through the optical sight is thereforev cos A where A is the angle of the target path with respect to the viewplane GB. The angular speed of the sight line is determined by dividingthe projection of the speed on the view plane by the associated radiusdistance, in other words, the target distance e. The angular speedtherefore becomes COS 5 Uz-COS A and must be proportional to the totaldirectioning signal C for the weapon to track the target:

7)z-COS A e (10) 2)z-0OS A sin 1:

v -cos A cos K e 12 Rearrangement of these equations yields:

v cos A. sin K=CH. (11a) v cos A. cos K=Cs.6 (12a) Equations 11a and maybe substituted into the lead angle Equations 8 and 9:

Because the lead angles are small, the following approXimations can bemade:

and

sin 8: 6

The final equations for the lead angle components are then 5H CH o andwhere e =initial distance,

t=time,

C=total directioning signal composed of two perpendicular components,and

r=total angle passed by the sight line since the beginning ofcalculation.

The total angle through which the sight line is rotated t =f Cat Thetotal directioning signal C is c= Cs +CH (4b) The initial distance ecorresponds to an amplification factor in the computer. When the initialvalue of the distance is available, the amplification factor is adjustedand the distance calculation starts at the time t=0.

Still unknown in the speed angle equation is the projectile speed vdependent on the kind of ammunition and on the distance e the projectilemust travel. For a particular kind of ammunition, the projectile speed vwill depend on the target distance e along the sight line, the positionA of the target path with relation to the weapon position and the speedv of the target. A reasonable approximation formula for the relationbetween the sight line distance e and the projectile speed v arrived atthrough calculations of the projectile speed for realistic values of e,v and A is The left side of the equation can be divided into twofactors:

where v =firing speed w=constant with dimensions of tlme sight distanceprojectile path distance less than 1 will not be considered as thiswould only be the case when the target was departing from the weaponposition. The practical maximum value In for the ratio is 1.25 whichresults at the greatest distance (2 with maximum target speed and adirect approach ()\=90). It is therefore reasonable to represent e/e bya function having a value between 1 and the maximum value m for thegreatest distance 2 diminishing towards 1 at decreasing distance e. Forinstance:

Values of the ratio Substituting this equation into Equation 12a:

e e 8G 6 further resulting in i" e(m1) 1+ 2e 13) If the left side of theabove equation is plotted with respect to e, a smooth, slightly curvedfunction will result which may be duplicated electronically.

Equations have thus been provided for calculation of the desiredvertical and lateral lead angles in a computer from the directioningsignals C and C and the initial distance s Consideration must now begiven to the target path rectangular speed components as viewed throughthe optical sight. The relationship between the two components determinethe direction of the resulting motion of the sight line necessary tofollow the target due to the inclination of the target path plane.Components of the inertial angular speed of the sight line necessary fortarget tracking indicate the inclination K of the target path plane by:

Qs tan K CS FIG. 3a is a representation of the target path as seenthrough the optical sight under normal conditions, i.e., the supportingmeans for the weapon in a level condition. In this condition, of course,cross hair F will be vertical (along a radius line of the earth) andcross hair F will be horizontal (tangent to the earths surface).

In following the target with the cross hair the inertial angular speedsof the sight line in the two orthogonal directions are indicative of theinstantaneous inclination angle at any point. For target movement in thefield of sight plane GE in the direction f, the orthogonal inertialangular speeds generated by movement of the sight line in the direction1" are indicative of the inclination angle K1.

As previously mentioned, the two orthogonal angular speed components ofthe sight line may be generated by means of a single rate gyro fixedlymounted along the axis of the sight line.

It is also possible to derive the angular speed signals from the controlvoltages generated by the sight optic drive. For example, stabilizationsystems utilizing integrating rate gyros to correct for changes inorientation of the turning plane of the weapon (due to a tank-mountedweapon traversing hilly ground, for example) require that the controlsignals to the sight drive be proportional to the angular speed of thesight line. The inclination angle of the target path plane may thereforebe evaluated according to the Equation 14 using these signals.

It is also necessary that the lead computer give the correct values whenthe weapon is in motion. As the normal target is an airplane and theweapon is mounted on a surface craft, the relative speed between targetand weapon is almost entirely determined by the speed of the target. Thespeed of the weapon may be neglected. Rotation of the weapon supportvehicle can be taken as a vector consisting of three components inmutually perpendicular planes. The axes of rotation for the threecomponents are the sight line r, a line it perpendicular to r andparallel to the turning plane AE, and the axis w which is perpendicularto both r and u. Rotational components around axes other than the sightline r may be easily compensated for by a stabilization system. Thesystem is not explained in detail here since it is not a part of thepresent invention. In general, rotation around the sight line r is notof interest for stabilization purposes. Therefore, no sensing means(gyro) is provided for this purpose. Rotation of the weapon supportvehicle around the sight line r can be expected to cause no reaction bythe stabilization system.

In the absence of the lead computer, the weapon would be directed in aline parallel to the sight line. With the interconnection of the leadcomputer, the axis of the weapon has a lead angle inclination withrespect to the sight line. Rotation of the craft around the sight lineaxis causes the axis of the weapon to trace a cone shaped shell aroundthe sight line. As long as the target is maintained in the cross hair bythe gun pointer, this condition has no effect. This is explained withreference to the drawings.

FIG. 3a represents the view through the optical sight with thehorizontal cross hair F (parallel to turning plane AB) in a horizontalposition with respect to the earth. To maintain the target at the pointof intersection of the cross hairs, the sight must be moved along theline 1" at an angle K1 with respect to the horizontal F For thecondition illustrated in FIG. 3a, that is, horizontal cross hair F(which is parallel to the turning plane of the weapon) level, theinertial angular speeds in the vertical and lateral direction formaintaining the target at the intersection of the cross hairs will havethe ratio Referring now to FIG. 3b, a roll motion through the angle Alcaround the sight line causes the cross hairs of the optical sight to bepositioned relative to a horizontal line as shown. Moving the opticalsight along the pre viously correct line as determined by the angle K1would lose the target moving along the line f. To maintain the sight ontarget, the gun pointer must change the relationship of the angularspeeds of the sight line so that the sight line again moves along theline f. The line f is now defined in position by the relationship Thischange in the angle 1: necessary for following of the target isautomatically calculated within the lead computer. The lead computertherefore not only computes the necessary lead angle but also theabsolute direction of the lead for any position of the weapon turningplane (e.g., tank traversing hilly ground or ship in rolling seas) andautomatically adjusts the weapon position according to the calculations.

The signals which are generated with a change of the directioning handleby the gun pointer correspond to new nominal values of the angularrotation speeds C and C of the weapon which are fed to the leadcomputer. Signals proportional to the inertial angular speeds may betaken from a rate gyro which is fixedly aligned with respect to the lineof sight. Rolling motion of the sight optic around the sight line doesnot change the ratio of the inertial angular speed components because,with the change of orientation of the rate gyro, the turning speed ofthe sight line as represented by two orthogonal components also changes.

With reference to FIG. 5, the operation of the preferred embodiment ofthe lead computer will be described. As previously described withrespect to Equations la and 2a, evaluation of the lead angle requiresthat the quantities C C and e/v be fed into the lead computer. Thesignal C is proportional to the angular speed 1; of the sight line inthe lateral direction and the signal C is proportional to the angularspeed 0. in the vertical direction. Utilizing Equation 4a for the totaldirectioning handle signal C the resultant angular speed is given byFIG. 5 does not show the source of the signals which are proportional tothe angular speeds. The block diagram begins with the signals applied toterminals 1 and 2 in the form of electrical control signals. It haspreviously been explained with reference to FIG. 4a that these signalsrepresenting the two components of the total directioning handle signalC can be used to calculate the total directioning signal C bygeometrical addition according to Equation 4b. In FIG. 5, the twosignals C and C are geometrically added in the circuit 3 providing onoutput lead 4 the signal C. The method of geometrical addition is notimportant and can be achieved in different ways as by squaring the inputsignals with subsequent adding and taking the square root or by additionof two AC voltages subjected to a ninety degree phase shift andrectification.

The signal on output lead 4 is representative of the angular speed ofthe sight line as shown in Equations 4b and 40. This signal isintegrated in circuit 5 and is also multiplied by a time proportionalsignal I in multiplier circuit 6. Generation of the signal t isaccomplished in integrator circuit 7 which is fed by constant signal UOn lead 31 at the output of integrator the signal 0' is available whichin a subsequent sine transformer 8 is transformed to the signal sin aappearing on lead 32. We now have available the dividend sin a and thedivisor t-C of the fraction in the Equation 4a which are fed toa dividercircuit 9 to derive the quantity sin 6/ C -t on lead 26. It is necessaryto have a signal which is proportional to the initial distance e alongthe sight line as shown in Equation 4a. Multiplication circuit 11 is fedwith an initial distance signal e which is multiplied with the signal onlead 26.

It will be realized that the hit probability of the weapon system willbe increased with a periodically varying signal corresponding todistance heterodyned with the lead signals. In the present embodiment,this is accomplished through modulation of the signal corresponding tothe initial distance e before it is fed to the multiplication circuit11. e is applied to terminal which is connected to the input of amodulation circuit 12 providing on output lead 27 the signalcorresponding to the equation The output of multiplier circuit 11 onlead 36 is now a function of time wherein e is proportional to thetarget distance along the sight line.

Reference to the Equations la and 2a necessary for the calculation ofthe lead angles 5 and 6 show that the signal e must still be divided bythe averaged projectile speed v and subsequently be multiplied by therespective directioning handle signal C and C As previously noted, theaverage projectile speed VG depends on several quantities and, for thelead angle calculations, the speed is not needed explicitly, but onlytogether with the target distance in the fraction e/v The dependence ofv and e/v on the dilferent param eters 'was investigated. It was foundthat the function can be represented by a group of curves approximatedby third degree parabolas. It is therefore possible to determine thedesired quantity e/v without evaluating the average projectile speed vusing only the target distance e. This is accomplished by feeding thesignal e(t) to a non-linear circuit 13 having the characteristictransfer 'function f(e). The output of non-linear circuit 13 appears onlead 37: the signal e/v previously modulated in circuit 12.

In accordance with Equations la and 2a, it is necessary to multiply thesignal with the associated directioning signals C and C to arrive at thesignal corresponding to the lead angle of the weapon in the vertical andlateral directions respectively. It is to be remembered that the leadangles of the weapons are always with reference tothe sight line whichis directed towards the target. Two multiplication circuits are providedin 14 and 15. Multiplier circuit 14 has as inputs the quotient e/v andthe lateral directioning signal C providing at the output on lead 39 thelateral lead signal of the weapon It would be possible to feed thissignal directly to the weapon, however, as the weapon itself cannot beturned in a lateral direction, but only can be elevated within arotatable turret, it is necessary to recalculate the lead signal withrespect to the lateral lead angle 6 of the turret according to Equation3a. Equation 3a shows that the elevation angle 0 of the sight line withrespect to the horizontal turning plane of the turret must be known. Toprovide this input information, the input of resolver 17 is coupledmechanically to provide a signal proportional to the elevation angle HThe resolver 17, provided with an alternating voltage of constantfrequency and amplitude, provides an output signal modulated inaccordance with the cosine of the elevation angle G The resolver outputsignal is fed to a demodulator 18 through lead 40 where it is rectifiedto provide cos O on lead 41. Cos Q is also fed to the division circuit20 through lead 19, providing on lead 21 at the output of dividercircuit 20 the lateral lead angle 6;; of the turret according to theEquation 3a:

K COS 05 It will be noted with reference to the previously citedEquation 5 that the factor e/v has been extracted from the product. Thequantity VG remains as a factor in the denominator of the fraction. Inthe above equation it has been designated V which has an average valuecorresponding to the average projectile speed at the main battledistance. Due to this simplification, the calculation of A requires onlythat the signal cos O (already calculated in the circuits 17 and 18) andthe value of e/v (at the output 37 of circuit 13) be multiplied with aconstant factor g/ZV The angle including the ballistic superelevation isdetermined by adding Equations 1a and 5a resulting in:

*=1( l. H vs CH+ZUGI Q V1: The signal cos 0 is multiplied by constantfactor is present while on the other input line 25, the directioningsignal C in the vertical direction is applied from input terminal 2through lead 25. The sum of the two input signals is connected tomultiplication circuit through lead 42. The signal e/v is multipliedwith the sum of the two signals providing, on lead 28 at the output ofthe multiplier circuit, the vertical lead signal 5 including theballistic superelevation according to the Equation 4a. The signal 5determines the lateral lead of the weapon with respect to the sightline. The lateral lead angle 6 of the turret determines the anglebetween the turret and the sight line. Due to the modulation of theinitial distance signal 2 the lateral lead angle as well as the verticallead angle vary in accordance with the amplitude of the modulation,which is dependent on the initial distance e It is to be realized inaccordance with the present invention, that the modulation may beomitted completely or it may be introduced at another point in thecircuit. In the embodiment shown in FIG. 5, the lateral variation andthe vertical variation of the lead angles are always at an equalpercentage. This appears to be the desirable situation, however it canbe modified.

In accordance with the invention, it shall be noted that thecomputations accomplished with the embodiment shown in FIG. 5 can alsobe realized with other electrical circuits. The equations could besolved, for example, by means of an analog computer. The trigonometrictransformation could be accomplished by resolvers or coordinate changersor a sine or cosine potentiometer. The servo-circuits are not to belimited to operation on alternating currents but also can be operatedusing direct current. The operation with DC causes a change ofrotational direction of the motors in response to a change in polarityof the applied current. With AC operation, the change of the motordirection is achieved by altering the phase of the carrier frequency inrelation to a reference phase. In both cases it is desirable tointroduce a low frequency alternating current to the direct current orthe carrier frequency. The present invention provides a system forcomputation of the lead angle but is not to be limited in scope by theembodiment shown. Various modifications of the system will be evident tothose skilled in the art while maintaining the essence of the presentinvention. It is our intention to be limited in scope only by theappended claims.

We claim:

1. A weapon fire control system wherein a biaxial directionable weaponand a biaxial directionable sight mounted on a movable platform areinterconnected electrically, including a lead angle computer interposedin e @kClIical interconnection whereby, in accordance with electricalsignals processed in said lead computer, said weapon is directed towarda target seen through said sight, said lead computer comprising:

first and second input means for receiving a signal proportional to theinertial angular speed of the sight line in a lateral and verticaldirection respectively; time dependent input; geometrical addition meansconnected to said first and second input means, having an output, forcomputing the geometrical sum of said signals; integrator meansconnected to said time dependent input, having an output, for providinga signal proportional to time which is the integral of a signal 7applied to said time dependent input; computer means, connected to saidoutput of said geometrical addition means and to said output of saidintegrator means, having an output for providing a signal directlyproportional to the sine of said signal at said output of saidgeometrical addition means and inversely proportional to the product ofsaid signals at said output of said integrator and said output of saidgeometrical addition means; first multiplier circuit having a firstinput connected to said output of said computer means and having asecond input, further having an output; initial distance input means forreceiving an electrical signal proportional to the target distance,connected to said second input of said first multiplier circuit, wherebysaid output of said multiplier circuit provides a signal directlyproportional to the product of the signal applied to said first inputand said signal applied to said initial distance input means; non-linearcircuit means with a predetermined transfer characteristic having inputand output whereby a signal at said input provides an output signal atsaid output in accordance with a predetermined nonlinear functionapproximating a parabola of the third degree, whereby the signal at saidoutput means of said non-linear circuit means is directly proportionalto the distance of the target and inversely proportional to the averagespeed of the projectile; second multiplier circuit having first andsecond input further having an output, said first input connected tosaid output of said non-linear circuit means and said second inputconnected to said first input means for receiving a signal proportionalto said inertial angular speed of said sight line in said lateraldirection, whereby a signal is provided at said output of said secondmultiplier circuit proportional to the desired lateral lead angle of theweapon with respect to the sight line; resolver means having amechanical input connected to said sight, further having an electricaloutput, whereby the signal at said electrical output is proportional tothe cosine of the elevation angle of said sight; first divider meansconnected to said output of said second multiplier circuit and furtherconnected to said output of said resolver means, having an outputcoupled to the lateral directioning apparatus of said weapon whereby thesignal at said output is directly proportional to said signal at saidoutput of said second multiplier circuit and is inversely proportionalto said signal at said electrical output of said resolver means;amplifier means, having an input and an output, said input connected tosaid output of said resolver means, for providing a signal at saidoutput of said amplifier means directly proportional to a signal at saidinput in accordance with a predetermined multiplication -factor; summingamplifier having first and second inputs and an output, said first inputconnected to said second input means for receiving a signal proportionalto the inertial angular speed of said sight line in a verticaldirection, said second input connected to said output of said amplifiermeans, said output of said summing amplifier providing a signal equal tothe sum of the signals at said first and second inputs; and

third multipler circuit means, having a first input connected to saidoutput of said non-linear circuit means, having a second input connectedto said output of said summing amplifier, having an output connected tothe vertical directioning apparatus for said weapon, for providing asignal to position said weapon in the vertical direction with respect tosaid sight line, whereby the combination of said lateral and saidvertical directioning signals provides direction of the weapon withrespect to said sight line at the correct angle for maximum bitprobability.

2. Apparatus as recited in claim 1 including means for modulating saidlateral and said vertical directioning signals.

3. Apparatus as recited in claim 1 wherein said predeterminedmultiplication factor of said amplifier means is adjusted in accordancewith the ballistic super elevation needed for a projectile fired fromsaid weapon.

4. A lead computer for an electrically positioned antiaircraft weaponsystem including a biaxially directionable Weapon and a biaxiallydirectionable sight line comprising:

input means for receiving signals proportional to the inertial angularspeeds C and C of said sight line; initial distance input means forreceiving a signal proportional to target distance at first contact;first signal processing means, connected to said initial distance inputmeans and to said input means, for evaluating the instantaneous targetdistance e;

second signal processing means, connected to said input means and tosaid first signal processing means, for evaluating the vertical leadangle 6 of said weapon using the equation where VG is the averageprojectile speed;

third signal processing means, connected to said input means and to saidfirst signal processing means, for evaluating the lateral lead angle 6of said weapon using the equation 14 turret carrying said weapon inaccordance with the equation sin 6 SlIl 5 evK 6. Apparatus as recited inclaim 4 wherein said second signal processing means and said thirdsignal processing means include non-linear circuit means for calculatingthe ratio e/v 7. Apparatus as recited in claim 4 including modulatingmeans for modulating said vertical lead angle and said lateral leadangle.

8. Apparatus as recited in claim 7 wherein said modulating means isconnected to said initial distance input means for modulating saidsignal proportional to target distance at first contact.

9. Apparatus as recited in claim 4 wherein said signals proportional tothe inertial angular speeds C and C of said sight line are generated bya rate gyro fixedly mounted with respect to said sight line.

10. Apparatus as recited in claim 4 wherein said signals proportional tothe inertial angular speeds C and C of said sight line are derived froman electric directioning handle for said sight line.

11. Apparatus as recited in claim 4 wherein said vertical lead angle oof said weapon is evaluated according to the approximate equation forsmall lead angles 6 5H CH and said lateral lead angle 6 of said weaponis evaluated according to the approximate equation for small lead anglesEUGENE G. BOLTZ, Primary Examiner R. W. WEIG, Assistant Examiner U.S.Cl. X.R. 89-l, 41

